1 / 42

Mixtures of Gaussians and Advanced Feature Encoding

Mixtures of Gaussians and Advanced Feature Encoding. Computer Vision CS 143, Brown James Hays. Many slides from Derek Hoiem , Florent Perronnin , and Hervé Jégou. Why do good recognition systems go bad?. E.g. W hy isn’t our Bag of Words classifier at 90% instead of 70%? Training Data

rickd
Download Presentation

Mixtures of Gaussians and Advanced Feature Encoding

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mixtures of Gaussians and Advanced Feature Encoding Computer Vision CS 143, Brown James Hays Many slides from Derek Hoiem, FlorentPerronnin, and HervéJégou

  2. Why do good recognition systems go bad? • E.g. Why isn’t our Bag of Words classifier at 90% instead of 70%? • Training Data • Huge issue, but not necessarily a variable you can manipulate. • Learning method • Probably not such a big issue, unless you’re learning the representation (e.g. deep learning). • Representation • Are the local features themselves lossy? Guest lecture Nov 8th will address this. • What about feature quantization? That’s VERY lossy.

  3. Standard Kmeans Bag of Words http://www.cs.utexas.edu/~grauman/courses/fall2009/papers/bag_of_visual_words.pdf

  4. Today’s Class • More advanced quantization / encoding methods that represent the state-of-the-art in image classification and image retrieval. • Soft assignment (a.k.a. Kernel Codebook) • VLAD • Fisher Vector • Mixtures of Gaussians

  5. Motivation • Bag of Visual Words is only about counting the number of local descriptors assigned to each Voronoi region • Why not including other statistics? http://www.cs.utexas.edu/~grauman/courses/fall2009/papers/bag_of_visual_words.pdf

  6. We already looked at the Spatial Pyramid level 2 level 1 level 0 But today we’re not talking about ways to preserve spatial information.

  7. Motivation • Bag of Visual Words is only about counting the number of local descriptors assigned to each Voronoi region • Why not including other statistics? For instance: • mean of local descriptors http://www.cs.utexas.edu/~grauman/courses/fall2009/papers/bag_of_visual_words.pdf

  8. Motivation • Bag of Visual Words is only about counting the number of local descriptors assigned to each Voronoi region • Why not including other statistics? For instance: • mean of local descriptors • (co)variance of local descriptors http://www.cs.utexas.edu/~grauman/courses/fall2009/papers/bag_of_visual_words.pdf

  9. Simple case: Soft Assignment • Called “Kernel codebook encoding” by Chatfield et al. 2011. Cast a weighted vote into the most similar clusters.

  10. Simple case: Soft Assignment • Called “Kernel codebook encoding” by Chatfield et al. 2011. Cast a weighted vote into the most similar clusters. • This is fast and easy to implement (try it for Project 3!) but it does have some downsides for image retrieval – the inverted file index becomes less sparse.

  11. A first example: the VLAD ① assign descriptors  2 1 • Given a codebook ,e.g. learned with K-means, and a set oflocal descriptors : •  assign: •  compute: • concatenate vi’s + normalize  3  4 x  5 ② compute x-  i ③ vi=sum x-  i for cell i v5 v1 v2 v3 v4 Jégou, Douze, Schmid and Pérez, “Aggregating local descriptors into a compact image representation”, CVPR’10.

  12. A first example: the VLAD • A graphical representation of Jégou, Douze, Schmid and Pérez, “Aggregating local descriptors into a compact image representation”, CVPR’10.

  13. The Fisher vectorScore function • Given a likelihood function with parameters , the score function of a given sample X is given by: •  Fixed-length vector whose dimensionality depends only on # parameters. • Intuition: direction in which the parameters  of the model should we modified to better fit the data.

  14. Aside: Mixture of Gaussians (GMM) • For Fisher Vector image representations,is a GMM. • GMM can be thought of as “soft” kmeans. • Each component has a mean and a standard deviation along each direction (or full covariance) 0.05 0.4 0.5 0.05

  15. This looks like a soft version of kmeans!

  16. The Fisher vectorRelationship with the BOV • FV formulas: 0.05 0.4 0.5 0.05 Perronnin and Dance, “Fisher kernels on visual categories for image categorization”, CVPR’07.

  17. The Fisher vectorRelationship with the BOV • FV formulas: • gradient wrt to w ≈  soft BOV = soft-assignment of patch t to Gaussian i 0.05 0.4 0.5 0.05 Perronnin and Dance, “Fisher kernels on visual categories for image categorization”, CVPR’07.

  18. The Fisher vectorRelationship with the BOV • FV formulas: • gradient wrt to w ≈  soft BOV = soft-assignment of patch t to Gaussian i  compared to BOV, include higher-order statistics (up to order 2) • Let us denote: D = feature dim, N = # Gaussians • BOV = N-dim • FV = 2DN-dim • gradient wrt to  and  0.05 0.4 0.5 0.05 Perronnin and Dance, “Fisher kernels on visual categories for image categorization”, CVPR’07.

  19. The Fisher vectorRelationship with the BOV • FV formulas: • gradient wrt to w ≈  soft BOV = soft-assignment of patch t to Gaussian i  compared to BOV, include higher-order statistics (up to order 2) • FV much higher-dim than BOV for a given visual vocabulary size • FV much faster to compute than BOV for a given feature dim • gradient wrt to  and  0.05 0.4 0.5 0.05 Perronnin and Dance, “Fisher kernels on visual categories for image categorization”, CVPR’07.

  20. The Fisher vectorDimensionality reduction on local descriptors • Perform PCA on local descriptors: •  uncorrelated features are more consistent with diagonal assumption of covariance matrices in GMM •  FK performs whitening and enhances low-energy (possibly noisy) dimensions

  21. The Fisher vectorNormalization: variance stabilization •  Variance stabilizing transforms of the form: • (with =0.5 by default) • can be used on the FV (or the VLAD). •  Reduce impact of bursty visual elements • Jégou, Douze, Schmid, “On the burstiness of visual elements”, ICCV’09.

  22. Datasets for image retrieval • INRIA Holidays dataset: 1491 shots of personal Holiday snapshot • 500 queries, each associated with a small number of results 1-11 results • 1 million distracting images (with some “false false” positives) • Hervé Jégou, Matthijs Douze and Cordelia Schmid • Hamming Embedding and Weak Geometric consistency for large-scale image search, ECCV'08

  23. ExamplesRetrieval • Example on Holidays: From: Jégou, Perronnin, Douze, Sánchez, Pérez and Schmid, “Aggregating local descriptors into compact codes”, TPAMI’11.

  24. ExamplesRetrieval • Example on Holidays: • second order statistics are not essential for retrieval From: Jégou, Perronnin, Douze, Sánchez, Pérez and Schmid, “Aggregating local descriptors into compact codes”, TPAMI’11.

  25. ExamplesRetrieval • Example on Holidays: • second order statistics are not essential for retrieval • even for the same feature dim, the FV/VLAD can beat the BOV From: Jégou, Perronnin, Douze, Sánchez, Pérez and Schmid, “Aggregating local descriptors into compact codes”, TPAMI’11.

  26. ExamplesRetrieval • Example on Holidays: • second order statistics are not essential for retrieval • even for the same feature dim, the FV/VLAD can beat the BOV • soft assignment + whitening of FV helps when number of Gaussians  From: Jégou, Perronnin, Douze, Sánchez, Pérez and Schmid, “Aggregating local descriptors into compact codes”, TPAMI’11.

  27. ExamplesRetrieval • Example on Holidays: • second order statistics are not essential for retrieval • even for the same feature dim, the FV/VLAD can beat the BOV • soft assignment + whitening of FV helps when number of Gaussians  • after dim-reduction however, the FV and VLAD perform similarly From: Jégou, Perronnin, Douze, Sánchez, Pérez and Schmid, “Aggregating local descriptors into compact codes”, TPAMI’11.

  28. ExamplesClassification • Example on PASCAL VOC 2007: From: Chatfield, Lempitsky, Vedaldi and Zisserman,“The devil is in the details: an evaluation of recentfeature encoding methods”, BMVC’11.

  29. ExamplesClassification •  FV outperforms BOV-based techniques including: • VQ: plain vanilla BOV • KCB: BOV with soft assignment • LLC: BOV with sparse coding • Example on PASCAL VOC 2007: From: Chatfield, Lempitsky, Vedaldi and Zisserman,“The devil is in the details: an evaluation of recentfeature encoding methods”, BMVC’11.

  30. ExamplesClassification •  FV outperforms BOV-based techniques including: • VQ: plain vanilla BOV • KCB: BOV with soft assignment • LLC: BOV with sparse coding •  including 2nd order information is important for classification • Example on PASCAL VOC 2007: From: Chatfield, Lempitsky, Vedaldi and Zisserman,“The devil is in the details: an evaluation of recentfeature encoding methods”, BMVC’11.

  31. Packages • The INRIA package: • http://lear.inrialpes.fr/src/inria_fisher/ • The Oxford package: • http://www.robots.ox.ac.uk/~vgg/research/encoding_eval/ • Vlfeat does it too! • http://www.vlfeat.org

  32. Summary • We’ve looked at methods to better characterize the distribution of visual words in an image: • Soft assignment (a.k.a. Kernel Codebook) • VLAD • Fisher Vector • Mixtures of Gaussians is conceptually a soft form of kmeans which can better model the data distribution.

More Related